Editing the inside of an object
To view an object from the inside, you have to be in the perspective camera mode, because you are not able to "enter" the object with an orthogonal camera.

The shortcut Numpad 5 let you switch between orthogonal camera and perspective camera.

also important is, to have backface culling disabled or else you wont see any backfaces . You can find it in the property panel in the 3dView (shortcut N). 



But if you really want to edit a inside of an object, I would recommend to create faces which are pointing inward to prevent issues while rendering.